We extend the notion of singular vectors to context Diophantine approximation real numbers with elements a totally number field K. For $$m\ge 1$$ , we establish version Dani’s correspondence in fields and prove that under class ‘friendly measures’ $$K_S^m$$ set has measure zero. Here S is Archimedean valuations K $$K_S$$ product completions $$\sigma (K)$$ \in S$$ . On other hand, show existence...

An interval number system is given by an initial interval cover of the extended real line and by a finite system of nonnegative Möbius transformations. Each sequence of transformations applied to an initial interval determines a sequence of nested intervals whose intersection contains a unique real number. We adapt in this setting exact real algorithms which compute arithmetical operations to a...

The problem of radio channel assignments with multiple levels of interference depending on distance can be modeled using graph theory. The authors previously introduced a model of labeling by real numbers. Given a graph G, possibly infinite, and real numbers k1, k2, . . . , kp ≥ 0, a L(k1, k2, . . . , kp)-labeling of G assigns real numbers f(x) ≥ 0 to the vertices x, such that the labels of ver...